Given: B is the midpoint of segment AC. AB = 3x - 1, BC = x +7
Find: The length of segment AC
22
02
011
Answers
Answer:
hope it helps
plz mark as brainliest
Length of [tex]\boldsymbol{AC}[/tex] is [tex]\boldsymbol{22}[/tex] units.
"To understand the calculation, check below."
Midpoint
The middle point of the a line segment is called the midpoint.
It's really the centroid of both segment and the ends, and it is equidistant from both.
It cuts the portion in half.
[tex]B[/tex] is the midpoint of [tex]
AC[/tex] [tex]\boldsymbol{AB=BC}[/tex][tex]3x-1=x+7[/tex] [tex]2x
AC=8[/tex] [tex]\boldsymbol{x=4}[/tex]
So,[tex]BC=4+7[/tex] [tex]=\boldsymbol{11}[/tex]
Therefore,[tex]AC=2BC[/tex] [tex]=2 \times 11\\=\boldsymbol{22}[/tex]Length of [tex]\boldsymbol{AC}[/tex] is [tex]\boldsymbol{22}[/tex] units.
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Related Questions
Endpoints of segment MN have coordinates (0, 0), (5, 1). The endpoints of segment AB have coordinates (1 1/22 , 2 1/4 ) and (−2 1/4 , k). What value of k makes these segments perpendicular?
Answers
Answer: [tex]k=18\dfrac{8}{11}[/tex].
Step-by-step explanation:
If a line passing through two points, then
[tex]Slope=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
Endpoints of segment MN have coordinates (0, 0) and (5, 1).
Slope of MN [tex]=\dfrac{1-0}{5-0}=\dfrac{1}{5}[/tex]
The endpoints of segment AB have coordinates [tex]\left(1\dfrac{1}{22} , 2\dfrac{1}{4}\right)[/tex] and [tex]\left(-2\dfrac{1}{4} , k\right)[/tex].
[tex]A=\left(1\dfrac{1}{22} , 2\dfrac{1}{4}\right)=\left(\dfrac{23}{22} ,\dfrac{9}{4}\right)[/tex]
[tex]B=\left(-2\dfrac{1}{4} , k\right)=\left(-\dfrac{9}{4} , k\right)[/tex].
Slope of AB [tex]=\dfrac{k-\frac{9}{4}}{-\frac{9}{4}-\dfrac{23}{22}}[/tex]
[tex]=\dfrac{\frac{4k-9}{4}}{\frac{-99-46}{44}}[/tex]
[tex]=\dfrac{4k-9}{4}\times \dfrac{44}{-145}[/tex]
[tex]=4k-9\times \dfrac{11}{-145}[/tex]
[tex]=\dfrac{44k-99}{-145}[/tex]
Product of slopes of two perpendicular segments is -1.
Slope of MN × Slope of AB = -1
[tex]\dfrac{1}{5}\times \dfrac{44k-99}{-145}=-1[/tex]
[tex]\dfrac{44k-99}{-725}=-1[/tex]
[tex]44k-99=725[/tex]
[tex]44k=725+99[/tex]
[tex]k=\dfrac{824}{44}[/tex]
[tex]k=\dfrac{206}{11}[/tex]
[tex]k=18\dfrac{8}{11}[/tex]
Therefore, the value of k is [tex]k=18\dfrac{8}{11}[/tex].
Answer:
k=21
Step-by-step explanation:
Find the slope of MN which is 1/5, (use the slope formula.)
Use the slope formula for AB using k as y_2
Substitute and you get k=21
21-2.25/-2.25-1.5=-5
The lines are perpendicular because the slopes are the negative reciprocal of one another.
Calculate the distance between the points (-8,1) and (0,7)
Answers
Answer:
10 units
Step-by-step explanation:
[tex]\boxed{distance = \sqrt{(x2 - x1)^{2} + (y2 - y1)^{2} }}[/tex]
Using the distance formula above,
distance between the 2 points
[tex] = \sqrt{[0 - ( - 8)]^{2} + (7 - 1)^{2} } \\ = \sqrt{(0 + 8)^{2} + 6^{2} } \\ = \sqrt{ {8}^{2} + 36} \\ = \sqrt{64 + 36} \\ = \sqrt{100} \\ = 10 \: units[/tex]
2. Multiply (-4)(-2)(-5). (5 points)
O
-40
O
-8
8
Answers
(8)(-5)=-40
Answer: -60
Step-by-step explanation: -4x-3x-5=-60...
x=40 and y=70 find value of z
Answers
Answer:
X=40 and y=70 if you add z you get 110 but I'm not really sure about this answer so you can also subtract it you get 30
Step-by-step explanation:
Give the correct name for
2x3 + 5x
Answers
Answer: x(2x²+5)
please give brainliest if it helped
Solve for n.
n + 1 = 4(6-8)
A.n=1
B.n=8
C.n=11
D.n=16
Answers
Simplify 6 - 8 to -2
n + 1 = 4 * -2
Simplify 4 * - 2 to -8
n + 1 = -8
Subtract 1 from both sides
n = -8 - 1
Simplify -8 - 1 to -9
n = -9
Check answer:
n + 1 = 4(6 - 8)
Let n = -9
-9 + 1 = 4 * (6 - 8)
Simplify 6 - 8 to -2
-9 + 1 = 4 * -2
Simplify 4 * -2 to -8
-9 + 1 = 8
n = 8
Answer:
n=9
Step-by-step explanation:
n+1=4(6-8)
We move all terms to the left:
n+1-(4(6-8))=0
We add all the numbers together, and all the variables
n+1-(4(-2))=0
We add all the numbers together, and all the variables
n+9=0
We move all terms containing n to the left, all other terms to the right
n=9
The answer should be n=9
I went to Half Priced Books and purchased 15 books. I paid $2 each for some and $3 each for the rest of the books. How many $2 books did I buy if I spent $34?
Answers
Answer:
Thus the number of books at $2 is 9 books.
Step-by-step explanation:
The number of the book purchased = 15 books
Total amount spend to buy the books = $34
The prices of books are $2 and $3.
Let the number of books purchased at price $2 = x
Let the number of books purchased at price $3 = y
Now we have to find the number of books that is bought at $2.
Below are the equations.
x + y = 15
2x + 3y = 34
Now solve for the x,
x + y = 15
y = 15 – x
Now insert it in the 2x + 3y = 34
2x + 3(15-x) = 34
2x + 45 – 3x = 34
-x = 34 – 45
x = 9
Thus the number of books at $2 is 9 books.
Ok this is not a solve, more of a vocab question. Whats the term used for the number circled? Like is that called a coefficient or something??
Answers
Answer:
I believe the term is the index number
Find the product (x+2t) exponent of 2
Answers
Answer:
x² + 4xtx + 4t²
Step-by-step explanation:
Given
(x + 2t)² = (x + 2t)(x + 2t)
Each term in the second factor is multiplied by each term in the first factor, that is
x(x + 2t) + 2t(x + 2t) ← distribute both parenthesis
= x² + 2tx + 2tx + 4t² ← collect like terms
= x² + 4tx + 4t²
The price of a dress in reduced by 60%. When the dress it is reduced by 60% of the reduced price. If the price of the dress after both reductions is 48$ what was the original price
Answers
Answer:
28.80$
Step-by-step explanation:
You are finding 60% of 48 because the question is asking what is the price of a 48 dollar item that is 60% off.
To ensure profits, a store is going to sell a sweater for 115 percent of the production cost. It costs $10 to make the sweater. Below are the calculations for finding the selling price. What mistake did the store owner make? (Original Cost)(Percent) = New Cost ($10)(0.115) = $1.15 The new cost is correct. The owner should have divided by 0.115. The owner should have multiplied by 11.5. The owner should have multiplied by 1.15.
Answers
Answer:I did the test and the answer is The owner should have multiplied by 1.15.
Step-by-step explanation:
Sample text
To make the calculation 115 percent of the production cost , the owner should have multiplied by 1.15 to the production cost.
What is percentage?" Percentage is defined as the hundredth part of any given number".
According to the question,
Production cost of a sweater = $10
To ensure profit , selling price = 115 percent of the production cost
(Original Cost)(Percentage)
[tex]= (10)(\frac{115}{100} )[/tex]
[tex]= $11.5[/tex]
Hence, to make the calculation 115 percent of the production cost , the owner should have multiplied by 1.15 to the production cost.
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Given the original statement "If a number is negative, the additive inverse is positive,” which are true? Select three options. If p = a number is negative and q = the additive inverse is positive, the original statement is p → q. If p = a number is negative and q = the additive inverse is positive, the inverse of the original statement is ~p → ~q. If p = a number is negative and q = the additive inverse is positive, the converse of the original statement is ~q → ~p. If q = a number is negative and p = the additive inverse is positive, the contrapositive of the original statement is ~p → ~q. If q = a number is negative and p = the additive inverse is positive, the converse of the original statement is q → p.
Answers
Answer:
The three options are;
1) If p = a number is negative and q = the additive inverse is positive, the original statement is p → q
2) If p = a number is negative and q = the additive inverse is positive, the original statement the inverse of the original statement is ~p → ~q
3) If q = a number is negative and p = the additive inverse is positive, the contrapositive of the original statement is ~p → ~q
Step-by-step explanation:
Given a statement if p then q, we have, p → q. The converse of the original statement is then, if q, then p while the inverse of the original statement is then if not p then not q, and the contrapositive statement is then if not q then not p
Mathematically, we have;
The given conditional statement;
If a number is negative, the additive inverse is positive which can be expressed as follows;
The conditional statement is p → q
The converse statement is q → p
The inverse statement is ~p → ~q
The contrapositive statement is ~q → ~p
Therefore, we have;
1) The conditional statement, if p = a number is negative and q = the additive inverse is positive, the original statement which is a conditional statement is therefore p → q
2) If p = a number is negative and q = the additive inverse is positive, the original statement, which is a conditional statement is p → q, the inverse of the original conditional statement is therefore, ~p → ~q
3) If q = a number is negative and p = the additive inverse is positive, the original statement, which is a conditional statement is therefore, q → p, the contrapositive of the original conditional statement is therefore ~p → ~q.
The three options are;
1) If p = a number is negative and q = the additive inverse is positive, the original statement is p → q
2) If p = a number is negative and q = the additive inverse is positive, the original statement the inverse of the original statement is ~p → ~q
3) If q = a number is negative and p = the additive inverse is positive, the contrapositive of the original statement is ~p → ~q
What is additive inverse?The additive inverse of any number is defined as when it is added to the number it gives zero as a result.
Given a statement if p then q, we have, p → q. The converse of the original statement is then, if q, then p while the inverse of the original statement is then if not p then not q, and the contrapositive statement is then if not q then not p
Mathematically, we have;
The given conditional statement;
If a number is negative, the additive inverse is positive which can be expressed as follows;
The conditional statement is p → q
The converse statement is q → p
The inverse statement is ~p → ~q
The contrapositive statement is ~q → ~p
Therefore, we have;
1) In The conditional statement, if p = a number is negative and q = the additive inverse is positive, the original statement which is a conditional statement is, therefore, p → q
2) If p = a number is negative and q = the additive inverse is positive, the original statement, which is a conditional statement is p → q, the inverse of the original conditional statement is, therefore, ~p → ~q
3) If q = a number is negative and p = the additive inverse is positive, the original statement, which is a conditional statement is, therefore, q → p, the contrapositive of the original conditional statement is, therefore, ~p → ~q
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Jack is fishing on a pier that is 2 feet above the water. When he casts his rod, the hook
on his line lands 8 feet below water. What is the total distance his hook traveled?
Answers
Answer:
10 feet
Step-by-step explanation:
2 + |-8| = 10
Hope this helps, have a great day:)
Explanation: 2 + 8 = 10
REPOST PLEASE HELP ME IVE BEEN WORKING FOREVER I CANT FAIL!!!
1. Bailey withdrew $135 from her checking account.
Part. If x represents the variable in the word problem above, explain what the variable should
represent
Part It: Write an algebraic expression to model the situation.
Part II: Bailey works part-time at a movie theater. The theater pays employees an hourly wage based
on their length of employment. Write an algebraic expression that describes how much Bailey's
employer pays part-time workers. SHOW WORK ON EVERYTHING!!!!!
Answers
Answer:
Step-by-step explanation:
Part 1: x represents her bank account
Part2: 135-x=y
Part 3: I'm not sure how long she's worked there, but it would look like: 7.85x=y. X representing number of hours
Help please picture attached
Answers
Answer:
-10
Step-by-step explanation:
3/5(b)=-6
Divide -6 by 3/5, you get -30/3.
solve for the equation 3x+2=8
Answers
I'm Pretty Sure The Answer Is x=2
Hope This Help's
Answer:
2
Step-by-step explanation:
When subtract the 2 from the right side and subtract it from the right side, then divide three from the left side and then divided it from the right side, then you should end up with x=2
During the summer, the height of the water in the pool decreased by 5 inches each week due to evaporation. What is the change in the height of the water over an 8 week period?
Answers
Answer:
40 inches
Step-by-step explanation:
We know that the height of water in a pool decreased 5 inches per week.
This means that we can form the equation [tex]y=-5x[/tex], since the amount of water remaining is proportionate to the amount of weeks that have passed.
We know [tex]x=8[/tex], since we need to find the change for 8 weeks.
[tex]y = -5\cdot 8[/tex]
[tex]-5 \cdot 8 = -40[/tex]
[tex]y=-40[/tex]
The change will be the absolute value of -40, which just makes it positive, so 40.
Hope this helped!
Answer:
40 inches evaporated
Step-by-step explanation:
5 in / week
Multiply 5 in by 8 wks
= 40 inches of water evaporated over 8 wks
What is the value of x?
-7.5 (x-3)=3.75
Answers
Answer:
x= 2.5
Step-by-step explanation:
-7.5 (x-3) = 3.75
(divide both sides of the equation by -7.5)
x-3 = -0.5
(move the constant to the righthand side and change the sign)
x = -0.5+3
(calculate the sum)
x = 2.5
Evaluate (f-g)(2)=?
Let f(x)=2x^2+8
g(x)=x-3
Answers
Answer:
[tex]\huge\boxed{(f-g)(2)=17}[/tex]
Step-by-step explanation:
[tex](f-g)(x)=f(x)-g(x)\\\\f(x)=2x^2+8;\ g(x)=x-3\\\\(f-g)(2)=f(2)-g(2)\\\\f(2)\ [g(2)]-\text{substitute}\ x=2\ \text{to}\ f(x)\ [g(x)]\\\\f(2)=2(2^2)+8=2(4)+8=8+8=16\\g(2)=2-3=-1\\\\(f-g)(2)=16-(-1)=16+1=17[/tex]
It rained 0.84 inches on Saturday and 0.8 inches on Sunday. How much did it rain on Saturday and Sunday combined?
Answers
Answer:
1.64
Step-by-step explanation:
The first step to do is to line up the decimal points. We have to add a zero to 0.8 so that the decimal points will align (this does not change the value).
0.84
+0.80
Then bring down the decimal point into the answer column, and add like normal.
0.84
+0.80
1.64
Hope this helps!
The smallest number by which 28 should be
multiplied so as to get a perfect square is
O2
O 4
03
07
Answers
Answer:
7
Step-by-step explanation:
28x7=196
196=14^2 aka a perfect square
4(n+9)-3(2+n)
Help now plz
Answers
Answer:
n + 30
Step-by-step explanation:
[tex]4(n+9)-3(2+n)\\\\\mathrm{Expand}\:4\left(n+9\right):\quad 4n+36\\=4n+36-3\left(2+n\right)\\\\\mathrm{Expand}\:-3\left(2+n\right):\quad -6-3n\\=4n+36-6-3n\\\\\mathrm{Simplify}\:4n+36-6-3n:\\\quad n+30[/tex]
Answer:
4n + 36 - 6 -3n
n + 30
Step-by-step explanation:
6. Solve the equation
Answers
steps ;
0.25(x+4) -3-28
remove the parentheses
0.25 x 1-3-28
calculate the difference
0.25x -30
hope this helped !!
One half of g plus thirty-two is as
much as the sum of fifteen and six times
g.
Answers
Answer:
g=34/11 0r g = 3.09 (approx)
Step-by-step explanation:
1/2g + 32 = 6g + 15
=> 32-15 = 6g-1/2g
=> 17 = 11/2g
=> 34/11 = g
or
g = 3.09 (approx.)
Plz answer this as soon as possible it’s my hw I have to submit it tomorrow.
Answers
Answer:
43
Step-by-step explanation:
-2+3×15
45-2
43 is the answer
Which set of side lengths represents a triangle with 3 lines of reflectional symmetry?
3, 4, 5
3, 6, 9
5, 5, 5
5, 10, 5
Answers
Answer:
5, 5, 5
Step-by-step explanation:
i saw it on quizlet
The set of side length that represents a triangle with 3 lines of reflectional symmetry is 5,5,5
Reflectional symmetry is a line that divides a triangle into halves. The halves the triangle are divided into are a reflection of each other.
A triangle is a shape that has three sides with three angles which sum up to 180 degrees.
Types of triangles :
Equilateral triangle : the three sides of the triangle have an equal length. It has three lines of reflectional symmetry Right-angled triangle : the square of the longest side is equal to the sum of the square of the other two sides Scalene triangle : all the three sides of the triangle have different lengths. It has no line of reflectional symmetry. Isosceles triangle ; it has two sides that have an equal length. It has one line of reflectional symmetryTo learn more about reflectional symmetry, please check: https://brainly.com/question/1593820?referrer=searchResults
any actives ???can y’all please help me
Answers
Answer:
B: $2.50
Step-by-step explanation:
Step 1: form an equation
126 = 12(8 + x)
Step 2: isolate the x
126/12 = 8 + x
126/12 - 8 = x
Step 3: solve
10.5 - 8 = x
2.5 = x = raise per hour
Mr.V's trail mix uses 1/2cup of peanuts, 2 1/4 cups raisins, and he uses 2 times more sunflower seeds than raisins.How many total cups of trail mix can mix can Mr.V make
Answers
Answer:
The total number of cups is 9 1/2 cups
Step-by-step explanation:
Here, we are interested in calculating the total cups of trail mix that Mr V can make.
From the question, we are told that he used 1/2 cups of peanuts, 2 1/4 cups of raisins and 2 times more sunflower seeds than raisins.
So basically, we need to find the number of cups of sunflower seeds used.
The information we have here is that he used 2 times more of raisins;
Thus, the number of cups of sunflower would be 2 * 2 1/4 = 2 * 9/4 = 9/2. But practically is 9/2 , two times more than 2 1/4? NO!
What we should do here is to add 9/2 to 2 1/4. In that case, the difference between the two will be 2 times the cups of raisins;
So 9/2 + 9/4 = (18 + 9)/4 = 27/4
So the total number of cups of trail mix that can be made will be;
1/2 + 27/4 + 9/4 = (2 + 27 + 9)/4 = 38/4 = 19/2 = 9 1/2 cups
Please help, question is in photo below, about finding angles.AWARDING MORE POINTS
Answers
The measure of angle ABC = ABD + DBC = 95 degrees.
Let's plug our values from the picture into our equation above.
95 = 2x + 23 + 9x - 5
Combine like terms
95 = 11x + 18
Subtract 18 from both sides
77 = 11x
Divide both sides by 11
7 = x
Angle ABD = 2x + 23 = 2(7) + 23 = 14 + 23 = 37 degrees.
Angle DBC = 9x - 5 = 9(7) - 5 = 63 - 5 = 58 degrees.
Steven wants to buy a $590 bicycle. Steven has no money saved, but will be able to deposit $50 into a savings account when he receives his paycheck each Friday. However, before Steven can buy the bike, he must give his sister $60 that he owes her. For how many weeks will Steven need to deposit money into his savings account before he can pay back his sister and buy the bike?
Answers
Answer:
13 weeks
Step-by-step explanation:
Add 590 and 60 together and then divide by 50 and you'll get 13